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Jun 27, 2018
06/18

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Javier Molina-Vilaplana

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We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor network. The results might help to understand how spacetimes may emerge from distributions of quantum...

Topics: Condensed Matter, Quantum Physics, Strongly Correlated Electrons, High Energy Physics - Theory

Source: http://arxiv.org/abs/1503.07699

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Jun 28, 2018
06/18

by
Javier Molina-Vilaplana

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The entanglement renormalization flow of a (1+1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.

Topics: Quantum Physics, Strongly Correlated Electrons, Condensed Matter, High Energy Physics - Theory

Source: http://arxiv.org/abs/1510.09020

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Sep 23, 2013
09/13

by
Javier Molina-Vilaplana

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The holographic mutual information $I_{AB}$ between two "small" coplanar and wide separated circular regions $A$ and $B$ in the four dimensional $\MN=4$ SYM gauge theory dual to Type IIB string theory in AdS$_5 \times S^5$, is computed. In our proposal, we first interpret the Ryu-Takayanagi prescription for the holographic computation of the entanglement entropy and the mutual information, in terms of submanifold observables associated with $k$-branes in the AdS/CFT correspondence....

Source: http://arxiv.org/abs/1305.1064v3

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Sep 23, 2013
09/13

by
Javier Molina-Vilaplana

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In this work we provide additional support for the proposed connection between the gauge/gravity dualities in string theory and the successful Multi-Scale-Entanglement-Renormalization-anstaz (MERA) method developed for the efficient simulation of quantum many body systems at criticality. This support comes by showing an explicit formal equivalence between the real space renormalization group (RG) flow of the two point correlation functions in different types of MERA states and the holographic...

Source: http://arxiv.org/abs/1109.5592v2

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Sep 22, 2013
09/13

by
Javier Molina-Vilaplana

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We investigate a recent conjecture connecting the AdS/CFT correspondence and entanglement renormalization tensor network states (MERA). The proposal interprets the tensor connectivity of the MERA states associated to quantum many body systems at criticality, in terms of a dual holographic geometry which accounts for the qualitative aspects of the entanglement and the correlations in these systems. In this work, some generic features of the entanglement entropy and the two point functions in the...

Source: http://arxiv.org/abs/1210.6759v2

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Jun 30, 2018
06/18

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Javier Molina-Vilaplana; Javier Prior

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We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA...

Topics: Quantum Physics, High Energy Physics - Theory, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1403.5395

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Sep 21, 2013
09/13

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Javier Molina-Vilaplana; Pasquale Sodano

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In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition...

Source: http://arxiv.org/abs/1108.1277v2

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Sep 23, 2013
09/13

by
Javier Molina-Vilaplana; Germán Sierra

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In this paper we formulate the $xp$ model on the AdS$_2$ spacetime. We find that the spectrum of the Hamiltonian has positive and negative eigenvalues, whose absolute values are given by a harmonic oscillator spectrum, which in turn coincides with that of a massive Dirac fermion in AdS$_2$. We extend this result to generic $xp$ models which are shown to be equivalent to a massive Dirac fermion on spacetimes whose metric depend of the $xp$ Hamiltonian. Finally, we construct the generators of the...

Source: http://arxiv.org/abs/1212.2436v4

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Jun 29, 2018
06/18

by
Jordan S. Cotler; Javier Molina-Vilaplana; Mark T. Mueller

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We upgrade cMERA to a systematic variational ansatz and develop techniques for its application to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a correspondence between the first two terms in the variational expansion and the Gaussian Effective Potential, we can exactly solve for a variational approximation to the cMERA entangler. As examples, we treat scalar $\varphi^4$ theory and the Gross-Neveu model and extract non-perturbative behavior. We also...

Topics: High Energy Physics - Theory, Quantum Physics

Source: http://arxiv.org/abs/1612.02427

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Sep 23, 2013
09/13

by
Francis N. C. Paraan; Javier Molina-Vilaplana; Vladimir E. Korepin; Sougato Bose

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We quantify the extractable entanglement of excited states of a Lieb-Liniger gas that are obtained from coarse-grained measurements on the ground state in which the boson number in one of two complementary contiguous partitions of the gas is determined. Numerically exact results obtained from the coordinate Bethe ansatz show that the von Neumann entropy of the resulting bipartite pure state increases monotonically with the strength of repulsive interactions and saturates to the impenetrable...

Source: http://arxiv.org/abs/1105.1211v3